Title: Inner Phases of Colloidal Hexagonal Spin Ice

Abstract

Using numerical simulations that mimic recent experiments on hexagonal colloidal ice, here we show that colloidal hexagonal artificial spin ice exhibits an inner phase within its ice state that has not been observed previously. Under increasing colloid-colloid repulsion, the initially paramagnetic system crosses into a disordered ice regime, then forms a topologically charge ordered state with disordered colloids, and finally reaches a threefold degenerate, ordered ferromagnetic state. This is reminiscent of, yet distinct from, the inner phases of the magnetic kagome spin ice analog. Finally, the difference in the inner phases of the two systems is explained by their difference in energetics and frustration.

We examine square and kagome artificial spin ice for colloids confined in arrays of double-well traps. Conversely, magnetic artificial spin ices, unlike colloidal and vortex artificial spin ice realizations, allow creation of doping sites through double occupation of individual traps. We find that doping square and kagome ice geometries produces opposite effects. For square ice, doping creates local excitations in the ground state configuration that produce a local melting effect as the temperature is raised. In contrast, the kagome ice ground state can absorb the doping charge without generating non-ground-state excitations, while at elevated temperatures the hopping of individual colloidsmore » is suppressed near the doping sites. Our results indicate that in the square ice, doping adds degeneracy to the ordered ground state and creates local weak spots, while in the kagome ice, which has a highly degenerate ground state, doping locally decreases the degeneracy and creates local hard regions.« less

We show that square and kagome artificial spin ices with disconnected islands exhibit disorder-induced nonequilibrium phase transitions. The critical point of the transition is characterized by a diverging length scale and the effective spin reconfiguration avalanche sizes are power-law distributed. For weak disorder, the magnetization reversal is dominated by system-spanning avalanche events characteristic of a supercritical regime, while at strong disorder, the avalanche distributions have subcritical behavior and are cut off above a length scale that decreases with increasing disorder. The different type of geometrical frustration in the two lattices produces distinct forms of critical avalanche behavior. Avalanches in themore » square ice consist of the propagation of locally stable domain walls separating the two polarized ground states, and we find a scaling collapse consistent with an interface depinning mechanism. In the fully frustrated kagome ice, however, the avalanches branch strongly in a manner reminiscent of directed percolation. We also observe an interesting crossover in the power-law scaling of the kagome ice avalanches at low disorder. Our results show that artificial spin ices are ideal systems in which to study a variety of nonequilibrium critical point phenomena as the microscopic degrees of freedom can be accessed directly in experiments.« less

Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical applications in microelectronics(1), such as data storage, memory and logic(2). However, it is difficult to achieve very high degeneracy, especially in a two-dimensional system(3,4). Here, we showcase in situ controllable geometric frustration with high degeneracy in a two-dimensional flux-quantum system. We create this in a superconducting thin film placed underneath a reconfigurable artificial-spin-ice structure(5). The tunable magnetic charges in the artificial-spin-ice strongly interact with the flux quanta inmore » the superconductor, enabling switching between frustrated and crystallized flux quanta states. The different states have measurable effects on the superconducting critical current profile, which can be reconfigured by precise selection of the spin-ice magnetic state through the application of an external magnetic field. We demonstrate the applicability of these effects by realizing a reprogrammable flux quanta diode. The tailoring of the energy landscape of interacting 'particles' using artificial-spin-ices provides a new paradigm for the design of geometric frustration, which could illuminate a path to control new functionalities in other material systems, such as magnetic skyrmions(6), electrons and holes in two-dimensional materials(7,8), and topological insulators(9), as well as colloids in soft materials(10-13).« less

Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals (SCs) in a nonfrustrated artificial geometrical lattice as a consequence of the structural confinement of skyrmions in magnetic potential wells. The emergent ice rules from the geometrically frustrated SCsmore » highlight a novel phenomenon in this skyrmion system: emergent geometrical frustration. We demonstrate how SC topology transitions between a nonfrustrated periodic configuration and a frustrated icelike ordering can also be realized reversibly. The proposed artificial frustrated skyrmion systems can be annealed into different ice phases with an applied current-induced spin-transfer torque, including a long-range ordered ice rule obeying ground state, as-relaxed random state, biased state, and monopole state. In conclusion, the spin-torque reconfigurability of the artificial skyrmion ice states, difficult to achieve in other artificial spin ice systems, is compatible with standard spintronic device fabrication technology, which makes the semiconductor industrial integration straightforward.« less

We examine the hopping dynamics of an artificial spin ice system constructed from colloids on a kagome optical trap array where each trap has two possible states. By applying an external drive from an electric field which is analogous to a biasing applied magnetic field for real spin systems, we can create polarized states that obey the spin-ice rules of two spins in and one spin out at each vertex. We demonstrate that when we sweep the external drive and measure the fraction of the system that has been polarized, we can generate a hysteresis loop analogous to the hystereticmore » magnetization versus external magnetic field curves for real spin systems. The disorder in our system can be readily controlled by changing the barrier that must be overcome before a colloid can hop from one side of a trap to the other. For systems with no disorder, the effective spins all flip simultaneously as the biasing field is changed, while for strong disorder the hysteresis curves show a series of discontinuous jumps or avalanches similar to Barkhausen noise.« less